/* erf.c  - public domain implementation of error function erf(3m)

reference - Haruhiko Okumura: C-gengo niyoru saishin algorithm jiten
(New Algorithm handbook in C language) (Gijyutsu hyouron
sha, Tokyo, 1991) p.227 [in Japanese]                 */
#include <stdio.h>
#include <math.h>

#ifdef _WIN32
# include <float.h>
# if !defined __MINGW32__ || defined __NO_ISOCEXT
#  ifndef isnan
#   define isnan(x) _isnan(x)
#  endif
#  ifndef isinf
#   define isinf(x) (!_finite(x) && !_isnan(x))
#  endif
#  ifndef finite
#   define finite(x) _finite(x)
#  endif
# endif
#endif

static double q_gamma(double, double, double);

/* Incomplete gamma function
1 / Gamma(a) * Int_0^x exp(-t) t^(a-1) dt  */
static double p_gamma(double a, double x, double loggamma_a)
{
	int k;
	double result, term, previous;

	if (x >= 1 + a) return 1 - q_gamma(a, x, loggamma_a);
	if (x == 0)     return 0;
	result = term = exp(a * log(x) - x - loggamma_a) / a;
	for (k = 1; k < 1000; k++) {
		term *= x / (a + k);
		previous = result;  result += term;
		if (result == previous) return result;
	}
	fprintf(stderr, "erf.c:%d:p_gamma() could not converge.", __LINE__);
	return result;
}

/* Incomplete gamma function
1 / Gamma(a) * Int_x^inf exp(-t) t^(a-1) dt  */
static double q_gamma(double a, double x, double loggamma_a)
{
	int k;
	double result, w, temp, previous;
	double la = 1, lb = 1 + x - a;  /* Laguerre polynomial */

	if (x < 1 + a) return 1 - p_gamma(a, x, loggamma_a);
	w = exp(a * log(x) - x - loggamma_a);
	result = w / lb;
	for (k = 2; k < 1000; k++) {
		temp = ((k - 1 - a) * (lb - la) + (k + x) * lb) / k;
		la = lb;  lb = temp;
		w *= (k - 1 - a) / k;
		temp = w / (la * lb);
		previous = result;  result += temp;
		if (result == previous) return result;
	}
	fprintf(stderr, "erf.c:%d:q_gamma() could not converge.", __LINE__);
	return result;
}

#define LOG_PI_OVER_2 0.572364942924700087071713675675 /* log_e(PI)/2 */

double erf(double x)
{
	if (!finite(x)) {
		if (isnan(x)) return x;      /* erf(NaN)   = NaN   */
		return (x>0 ? 1.0 : -1.0);   /* erf(+-inf) = +-1.0 */
	}
	if (x >= 0) return   p_gamma(0.5, x * x, LOG_PI_OVER_2);
	else        return - p_gamma(0.5, x * x, LOG_PI_OVER_2);
}

double erfc(double x)
{
	if (!finite(x)) {
		if (isnan(x)) return x;      /* erfc(NaN)   = NaN      */
		return (x>0 ? 0.0 : 2.0);    /* erfc(+-inf) = 0.0, 2.0 */
	}
	if (x >= 0) return  q_gamma(0.5, x * x, LOG_PI_OVER_2);
	else        return  1 + p_gamma(0.5, x * x, LOG_PI_OVER_2);
}